Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Möbius iterated function systems


Author: Andrew Vince
Journal: Trans. Amer. Math. Soc. 365 (2013), 491-509
MSC (2010): Primary 28A80
Published electronically: August 7, 2012
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Iterated function systems have been most extensively studied when the functions are affine transformations of Euclidean space and, more recently, projective transformations on real projective space. This paper investigates iterated function systems consisting of Möbius transformations on the extended complex plane or, equivalently, on the Riemann sphere. The main result is a characterization, in terms of topological, geometric, and dynamical properties, of Möbius iterated function systems that possess an attractor. The paper also includes results on the duality between the attractor and repeller of a Möbius iterated function system.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 28A80

Retrieve articles in all journals with MSC (2010): 28A80


Additional Information

Andrew Vince
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: avince@ufl.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05624-8
PII: S 0002-9947(2012)05624-8
Keywords: Iterated function systems, Möbius transformation
Received by editor(s): April 8, 2011
Received by editor(s) in revised form: May 9, 2011
Published electronically: August 7, 2012
Additional Notes: Thanks go to Michael Barnsley for always stimulating conversations on iterated function systems, and for graciously hosting my visit to the Australian National University, where much of this paper was written.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.